Mi Zhao

An Elasto-Plastic Damage Model for Rocks Based on a New Nonlinear Strength Criterion

The strength and deformation characteristics of rocks are the most important mechanical properties for rock engineering constructions. A new nonlinear strength criterion is developed for rocks by combining the Hoek–Brown (HB) criterion and the nonlinear unified strength criterion (NUSC). The proposed criterion takes account of the intermediate principal stress effect against HB criterion, as well as being nonlinear in the meridian plane against NUSC. Only three parameters are required to be determined by experiments, including the two HB parameters σc and mi. The failure surface of the proposed criterion is continuous, smooth and convex. The proposed criterion fits the true triaxial test data well and performs better than the other three existing criteria. Then, by introducing the Geological Strength Index, the proposed criterion is extended to rock masses and predicts the test data well. Finally, based on the proposed criterion, a triaxial elasto-plastic damage model for intact rock is developed. The plastic part is based on the effective stress, whose yield function is developed by the proposed criterion. For the damage part, the evolution function is assumed to have an exponential form. The performance of the constitutive model shows good agreement with the results of experimental tests.

Short-crested, cnoidal, and solitary wave forces on composite bucket foundation for an offshore wind turbine

The analytical solutions for the diffraction of the short-crested wave, the cnoidal wave, and the solitary wave incident on a composite bucket foundation of an offshore wind turbine are derived in this paper. The analytical expressions for the pressure, wave run-up, and wave force on the composite bucket foundation are obtained. Based on the numerical results, it is found that the short-crested wave run-up is affected by the wave phase, the cnoidal wave run-up is affected by the wave parameter λ, and the solitary wave run-up is affected by the wave parameter χ. For a composite bucket foundation, the long-crested wave force is larger than the short-crested wave force and the solitary wave force is larger than cnoidal wave force in certain shallow water conditions. Moreover, the short-crested wave force may first increase and then decrease with the increase in the water depth, while the cnoidal wave force and the solitary wave force monotonically increase with the increase in the water depth. In the design of the offshore wind turbine with composite bucket foundation, it will be more conservative if the formula derived from the plane waves is used as design criteria in a short-crested sea, and the wave force in shallow water should be determined by the solitary wave and the cnoidal wave together.The analytical solutions for the diffraction of the short-crested wave, the cnoidal wave, and the solitary wave incident on a composite bucket foundation of an offshore wind turbine are derived in this paper. The analytical expressions for the pressure, wave run-up, and wave force on the composite bucket foundation are obtained. Based on the numerical results, it is found that the short-crested wave run-up is affected by the wave phase, the cnoidal wave run-up is affected by the wave parameter λ, and the solitary wave run-up is affected by the wave parameter χ. For a composite bucket foundation, the long-crested wave force is larger than the short-crested wave force and the solitary wave force is larger than cnoidal wave force in certain shallow water conditions. Moreover, the short-crested wave force may first increase and then decrease with the increase in the water depth, while the cnoidal wave force and the solitary wave force monotonically increase with the increase in the water depth. In the design ...

Seismic stability of jointed rock slopes under obliquely incident earthquake waves

Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves. However, for rock slopes, the earthquake waves might approach the outcrop still with a evidently oblique direction. To investigate the impact of obliquely incident earthquake excitations, the input method for SV and P waves with arbitrary incident angles is conducted, respectively, by adopting the equivalent nodal force method together with a viscous-spring boundary. Then, the input method is introduced within the framework of ABAQUS software and verified by a numerical example. Both SV and P waves input are considered herein for a 2D jointed rock slope. For the jointed rock mass, the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum. Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes. The larger the incident angle, the greater the risk of slope instability. Furthermore, the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily. P waves induce weaker responses and SV waves are shown to be more critical.